An approach-evasion differential game: Stochastic guide

An approach-evasion positional differential game is considered for a conflict-controlled motion and a target set within a given set. Use is made of a solution of the associated boundary-value problem for a parabolic equation degenerating as the diffusion term vanishes to a Hamilton-Jacobi type equation, which is typical for techniques in the theory of differential games. Based on this, a control scheme with a stochastic guide is developed.